Mathematical Operations?

Question

X and Y have different dimensions. For each of the statements below, select the operation is physically meaningful or not:

X + Y or X - Y

X² + Y²

X² or Y²

X^1/3 or Y^1/3

X/Y or X*Y

e^X/Y or e^X + Y

Answer 1

Cool ** Parth

I bet this one is not so hard, let's check it out.

First it is really a physics problem DISGUISED as a math problem.

It is all about what unit combinations are allowed.

(1)  5 meters + 3 seconds. Nope can not do that.

(2)  25 square meters + 3 square seconds. Nope does not make sense.

(3) 25 square meters. Yes, this makes sense, at least for length.

(4) Say X is 27 cubic meters. The cube root of that is 3 meters. Yes makes sense.

(5) 5 kilograms per meter  YES. And how about 15 kilogram-meters. Sure thing.

(6) No and No. Because the "power number" has to be unitless. For example if you had e^(12 meters/6 meters) that would be e^2 which is fine.

Thanks Parth for this great and interesting question.